Question

Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter your answers using interval notation.

Answer 1

Answer:

• Increasing: (4, ∞)

,

• Decreasing: (-∞. 4)

,

• Constant: DNE

Explanation:

Given the function:

$f(x)=x^2-8x$

First, find the derivative:

$f^{\prime}(x)=2x-8$

When f'(x)<0:

$\begin{gathered} 2x-8<0 \\ 2x<8 \\ x<\frac{8}{2} \\ x<4 \\ \implies(-\infty,4) \end{gathered}$

The interval of decrease is at (-∞, 4).

When f'(x)>0:

$\begin{gathered} 2x-8>0 \\ 2x>8 \\ x>\frac{8}{2} \\ x>4 \\ \implies(4,\infty) \end{gathered}$

The interval of increase is at (4, ∞).

There is no interval at which the function is constant, so we write DNE.